The impact of mean reversion of bank profitability on post-merger performance in the banking industry

This research study examines the tendency for serial correlation in bank holding company profitability, finding significant evidence of reversion to the industry mean in profitability. The paper then considers the impact of mean reversion on the evaluation of post-merger performance of bank holding companies. The research concludes that when an adjustment is made for the mean reversion, post-merger results significantly exceed those of the industry in the first 5 years after the merger.     

Analytical pricing of discrete arithmetic Asian options with mean reversion and jumps

Empirical evidence indicates that commodity prices are mean reverting and exhibit jumps. As some commodity option payoffs involve the arithmetic average of historical commodity prices, we derive an analytical solution to arithmetic Asian options under a mean reverting jump diffusion process. The analytical solution is implemented with the fast Fourier transform based on the joint characteristic function of the terminal asset price and the realized average value. We also examine the accuracy and computational efficiency of the proposed method through numerical studies.     

Testing for mean reversion in heteroskedastic data II: Autoregression tests based on Gibbs-sampling-augmented randomization

A decade ago Fama and French [Fama, E.G., French, K.R., 1988. Permanent and temporary components of stock prices. J. Political Econ. 96 (2) 246–273] estimated that 40% of variation in stock returns was predictable over horizons of 3–5 yr, which they attributed to a mean reverting stationary component in prices. While it has been clear that the Depression and war years exert a strong influence on these estimates, it has not been clear whether the large returns of that period contribute to the information in the data or rather are a source of noise to be discounted in estimation. This paper uses the Gibbs-sampling-augmented randomization methodology to address the problem of heteroskedasticity in estimation of multi-period return autoregressions. Extending the sample period to 1995, we find little evidence of mean reversion. Examining subsamples, only 1926–1946 provides any evidence of mean reversion, while the post war period is characterized by mean aversion. A test of structural change suggests that this difference between pre and post war periods is significant.     

Nonlinear mean reversion in stock prices

This paper provides new evidence on the time-series predictability of stock market returns by introducing a test of nonlinear mean reversion. The performance of extreme daily returns is evaluated in terms of their power to predict short- and long-horizon returns on various stock market indices and size portfolios. The paper shows that the speed of mean reversion is significantly higher during the large falls of the market. The parameter estimates indicate a negative and significant relation between the monthly portfolio returns and the extreme daily returns observed over the past one to eight months. Specifically, in a quarter in which the minimum daily return is −2% the expected excess return is 37 basis points higher than in a month in which the minimum return is only −1%. This result holds for the value-weighted and equal-weighted stock market indices and for each of the size decile portfolios. The findings are also robust to different sample periods, different indices, and investment horizons.     

Testing for mean reversion in heteroskedastic data II: Autoregression tests based on Gibbs-sampling-augmented randomization

A decade ago Fama and French [Fama, E.G., French, K.R., 1988. Permanent and temporary components of stock prices. J. Political Econ. 96 (2) 246–273] estimated that 40% of variation in stock returns was predictable over horizons of 3–5 yr, which they attributed to a mean reverting stationary component in prices. While it has been clear that the Depression and war years exert a strong influence on these estimates, it has not been clear whether the large returns of that period contribute to the information in the data or rather are a source of noise to be discounted in estimation. This paper uses the Gibbs-sampling-augmented randomization methodology to address the problem of heteroskedasticity in estimation of multi-period return autoregressions. Extending the sample period to 1995, we find little evidence of mean reversion. Examining subsamples, only 1926–1946 provides any evidence of mean reversion, while the post war period is characterized by mean aversion. A test of structural change suggests that this difference between pre and post war periods is significant.     

Mean reversion and the forecasting of country betas: a note

In 1971 and 1975, M. E. Blume found individual equity betas to have a “regression” tendency toward the grand mean of unity. His original results have been widely accepted to the extent that a literature has developed on the application of Bayesian techniques to beta estimation so as to adjust for mean reversion. The more recent literature has focused on risk estimation and the applicability of asset pricing models in the international finance setting, where the focus has been on the aggregate country level risk. Given the increasing popularity of country beta models, an interesting but, as yet, unexplored issue is whether aggregate country betas display mean reversion tendencies similar to that found for individual company betas. The examination of this issue is the central aim of the current paper. In short, this analysis reveals strong evidence of mean reversion of country betas, similar to that documented in the single country setting in the existing literature.     

Persistence and mean reversion in UK stock returns

This paper re-examines the issue of persistence and mean reversion in UK stock returns in the light of new developments published in Chow and Denning (1993) the random walk hypothesis is tested using multiple variance ratios for returns on the Financial Times All Share Index and 330 individual stocks for the period January 1965 to June 1994. There is no evidence of reversion in the UK stock market. Persistence only exists in high frequency data and is less strong in more recent times. Moreover, it is a portfolio phenomenon and is related to firm size. There is a possibility that persistence/reversion is also industry-related.     

Modelling fundamental analysis in portfolio selection

We derive a closed-form appraisal/information ratio of the investors who are able to observe some information about security fundamentals, by solving a simple instantaneous mean-variance portfolio choice problem in a continuous-time framework. Both analytical and numerical results suggest that investors should choose securities with a more volatile mispricing, a less volatile fundamental, a higher mean-reverting speed and a larger dividend. Our model calibrated with realistic parameters easily outperforms top-percentile portfolio managers in reality, which suggests that the implementation of fundamental analysis may be impeded in practice due to limits of arbitrage. Our paper is a first, necessarily simple, step towards filling the gap of modelling fundamental analysis in portfolio selection.     

Default risk premium and asset prices

We estimate a standard structural model of credit risk to draw insights about the premium demanded by investors for bearing default risk, using data on credit default swaps and market capitalization. We pin down the daily market value of assets for a set of non-financial firms and uncover cross-sectional heterogeneity in terms of the magnitude and time variation of the premium. By exploring the link between asset and default risk premia, we show that this heterogeneity closely depends on the relationship between the firm-specific market value of the assets and the business cycle.     

Mean reversion in international stock markets: An empirical analysis of the 20th century

This paper analyzes mean reversion in the stock markets of 18 OECD countries during the years 1900–2009. In this period it takes stock prices about 18.5 years, on average, to absorb half of a shock. However, using a rolling-window approach we establish large fluctuations in the speed of mean reversion over time. The highest mean reversion speed is found for the period including the Great Depression and the start of World War II. Furthermore, the early years of the Cold War and the period containing the Oil Crisis of 1973, the Energy Crisis of 1979 and Black Monday in 1987 are also characterized by relatively fast mean reversion. We document half-lives ranging between 2.0 and 22.6 years. Our results suggest that the speed at which stocks revert to their fundamental value is higher in periods of high economic uncertainty, caused by major economic and political events.     

On the positive fundamental value of money with short-sale constraints

This paper is concerned with the pricing of money in a framework with restrictions on trading, under an extension of the standard-asset pricing theory that recognizes both tangible and intangible returns. It is argued that the underlying motivations for demanding money give content to its fundamental value and the bubble component. This approach is illustrated by analyzing the case where no short-sales are allowed, as two examples from the literature are made used to assert that money is a pure pricing bubble. Owing to this setup exhibits technically incomplete financial markets, the fundamental value of money is not uniquely defined over the set of generalized state-price processes. Then, these examples are shown to comprise an extreme case, as money is a pure store of value for the state-prices chosen (i.e., it is a pricing bubble). Instead, the fundamental value of money can be positive for other state-prices, representing the role of money in the trading process. Therefore, money should not be considered the equivalent of a pure pricing bubble.      

Inferring fundamental value and crash nonlinearity from bubble calibration

Identifying unambiguously the presence of a bubble in an asset price remains an unsolved problem in standard econometric and financial economic approaches. A large part of the problem is that the fundamental value of an asset is, in general, not directly observable and it is poorly constrained to calculate. Further, it is not possible to distinguish between an exponentially growing fundamental price and an exponentially growing bubble price. In this paper, we present a series of new models based on the Johansen–Ledoit–Sornette (JLS) model, which is a flexible tool to detect bubbles and predict changes of regime in financial markets. Our new models identify the fundamental value of an asset price and a crash nonlinearity from a bubble calibration. In addition to forecasting the time of the end of a bubble, the new models can also estimate the fundamental value and the crash nonlinearity, meaning that identifying the presence of a bubble is enabled by these models. In addition, the crash nonlinearity obtained in the new models presents a new approach to possibly identify the dynamics of a crash after a bubble. We test the models using data from three historical bubbles ending in crashes from different markets. They are the Hong Kong Hang Seng index 1997 crash, the S&P 500 index 1987 crash (Black Monday) and the Shanghai Composite index 2009 crash. All results suggest that the new models perform very well in describing bubbles, forecasting their ending times and estimating fundamental value and the crash nonlinearity. The performance of the new models is tested under both the Gaussian residual assumption and non-Gaussian residual assumption. Under the Gaussian residual assumption, nested hypotheses with the Wilks' statistics are used and the p-values suggest that models with more parameters are necessary. Under the non-Gaussian residual assumption, we use a bootstrap method to obtain type I and II errors of the hypotheses. All tests confirm that the generalized JLS models provide useful improvements over the standard JLS model.     

Dependence and mean reversion in stock prices: The case of the MENA region

This paper provides empirical evidence on the long memory behavior of the stock markets of Egypt, Jordan, Morocco, and Turkey. To test for long memory in the returns and volatility, we employ the modified rescaled range statistic R/S proposed by Lo [Lo, A.W., 1991. Long-term memory in stock market prices. Econometrica 59, 1279–1313] and the recently proposed rescaled variance V/S statistic developed by Giraitis et al. [Giraitis, L., Kokoszka, P.S. Leipus, R., Teyssiere, G., 2003. Rescaled variance and related tests for long memory in volatility and levels. J. Econ. 112, 265–294]. Further analysis is conducted by employing the ARFIMA (p, d, q) model to estimate the long memory parameters. Egypt and Morocco show evidence of long memory in the return series, while Jordan and Turkey display negative persistence. For the volatility series, long memory is conclusively demonstrated for all markets. Then, we compare the forecasting performance of ARMA and ARFIMA models and find that the ARFIMA model outperforms in out-of-sample forecasting of the markets. Our results should be useful to regulators, practitioners and derivative market participants, whose success depends on the ability to forecast stock price movements in these markets.     

Conditional extreme risk,black swan hedging,and asset prices

Motivated by the asset pricing theory with safety-first preference, we introduce and operationalize a conditional extreme risk (CER) measure to describe expected stock performance conditional on a small-probability market downturn (black swan). We document a significant CER premium in the cross-section of expected returns. We also demonstrate that CER explains the premia to downside beta, coskewness, and cokurtosis. CER provides distinct information regarding black swan hedging that cannot be captured by co-crash-based tail dependence measures. As we find that the pricing effect is stronger among black swan hedging stocks, this distinction helps explain the absence of premium to tail dependence.     

Modeling the behavior of real asset prices

Recently there has been much research treating housing and other real assets as financial claims, primarily in order to value their derivative assets, such as mortgages and mortgage-backed securities. Real asset prices are then typically modeled as a lognormal process, in the same manner that has traditionally been applied to firm value. The service flow or implicit value of a house is thus considered, in analogy with stock dividends, to be a fixed proportion of the fluctuating house price. We consider the appropriateness of this formulation and draw some distinctions between real assets, such as a house, and investment enterprises, such as a firm. We then propose an alternative method of formulating the service flow and the price of real assets which seems more appropriate to the economic characteristic of such assets.     

Mean reversion of short-run interest rates: empirical evidence from new EU countries

This article deals with the analysis of the mean reversion property of short-term interest rates in Central and Eastern European countries, using daily data from January 2000 to December 2008. For this purpose, we use long memory (fractionally integrated) models, and employ non-parametric, semi-parametric and parametric techniques to check if our results are robust across different methods. The results indicate that the mean reversion only takes place in the case of Hungary. For the remaining countries, the short-term interest rates are clearly non-stationary and non-mean reverting. Allowing for one break in the data, the break date takes place about 2001/2003 in all the series except in Lithuania, where the break occurs in 2007. In general, we observe an increase in the degree of dependence after the break in the majority of the series.     

The impact of monetary policy on asset prices

Estimating the response of asset prices to changes in monetary policy is complicated by the endogeneity of policy decisions and the fact that both interest rates and asset prices react to numerous other variables. This paper develops a new estimator that is based on the heteroskedasticity that exists in high-frequency data. We show that the response of asset prices to changes in monetary policy can be identified based on the increase in the variance of policy shocks that occurs on days of FOMC meetings and of the Chairman's semi-annual monetary policy testimony to Congress. The identification approach employed requires a much weaker set of assumptions than needed under the “event-study” approach that is typically used in this context. The results indicate that an increase in short-term interest rates results in a decline in stock prices and in an upward shift in the yield curve that becomes smaller at longer maturities. The findings also suggest that the event-study estimates contain biases that make the estimated effects on stock prices appear too small and those on Treasury yields too large.     

A tale of two prices: Liquidity and asset prices in multiple markets

This paper investigates the liquidity effect in asset pricing by studying the liquidity–premium relationship of an American depositary receipt (ADR) and its underlying share. Using the [Amihud, Yakov, 2002. Illiquidity and stock returns: cross-section and time series effects. Journal of Financial Markets 5, 31–56] measure, the turnover ratio and trading infrequency as proxies for liquidity, we show that a higher ADR premium is associated with higher ADR liquidity and lower home share liquidity, in terms of changes in these variables. We find that the liquidity effects remain strong after we control for firm size and a number of country characteristics, such as the expected change in the foreign exchange rate, the stock market performance, as well as several variables measuring the openness and transparency of the home market.     

The effect of takeovers on the fundamental value of acquirers

This paper develops a new methodology to examine the financial impact of acquisitions, designed to address whether takeovers yield a positive net present value for the acquiring company. Specifically, we employ the residual income valuation method to compare the fundamental value of the acquiring company before acquisition with the fundamental value after acquisition.We apply this methodology to 303 UK acquisitions completed during 1985–1996, and compare the results with the effects of takeover on profitability and short‐ and long‐run share returns. We find that the impact of acquisition on fundamental value is slightly negative but statistically insignificant. This result differs from the effect of takeover on profitability, which is significantly positive, and the effect of takeover on share returns, which is significantly negative.